The biggest change in this new “Company” would be the central character of Bobby. Whereas he has always been a straight man struggling with commitment issues and multiple girlfriends, he has been reconceived by Mr. Tiffany as a gay man with commitment issues and multiple boyfriends. And some characters have had gender reversals; the character of Joanne, who sings “The Ladies Who Lunch” and was originally played by Elaine Stritch on Broadway, is being played by the Tony winner Alan Cumming (“Cabaret”) in Mr. Tiffany’s reading of the work at Roundabout this week.

For years Mr. Sondheim and the musical’s book writer, George Furth, who died in 2008, batted back suggestions that Bobby was furtively intended to be a closeted gay man. But when Mr. Tiffany proposed actually making Bobby gay, Mr. Sondheim said in a telephone interview on Tuesday, the idea intrigued him.

“It’s still a musical about commitment, but marriage is seen as something very different in 2013 than it was in 1970,” Mr. Sondheim said. “We don’t deal with gay marriage as such, but this version lets us explore the issues of commitment in a fresh way.”

The musical is currently being workshopped and will be performed for a private audience on Friday.

Daniel Evans will play Bobby and he'll be joined by other castmembers including Michael Urie, Bobby Steggert, and the aforementioned Cumming.